Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}3x-3y &= -3 \\ -3x-8y &= -5\end{align*}$
Explanation: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-11y = -8$ Divide both sides by $-11$ and reduce as necessary. $y = \dfrac{8}{11}$ Substitute $\dfrac{8}{11}$ for $y$ in the top equation. $3x-3( \dfrac{8}{11}) = -3$ $3x-\dfrac{24}{11} = -3$ $3x = -\dfrac{9}{11}$ $x = -\dfrac{3}{11}$ The solution is $\enspace x = -\dfrac{3}{11}, \enspace y = \dfrac{8}{11}$.